Summary: Learning semantic representation for translation context is beneficial to statistical machine translation (SMT). Previous efforts have focused on implicitly encoding syntactic and semantic knowledge in translation context by neural networks, which are weak in capturing explicit structural syntax information. In this paper, we propose a new neural network with a tree-based convolutional architecture to explicitly learn structural syntax information in translation context, thus improving translation prediction. Specifically, we first convert parallel sentences with source parse trees into syntax-based linear sequences based on a minimum syntax subtree algorithm, and then define a tree-based convolutional network over the linear sequences to learn syntax-based context representation and translation prediction jointly. To verify the effectiveness, the proposed model is integrated into phrase-based SMT. Experiments on large-scale Chinese-to-English and German-to-English translation tasks show that the proposed approach can achieve a substantial and significant improvement over several baseline systems.